There are many cases, both in signal and in image processing applications, where the eigenvalues and vectors of particular matrix operators are required. Furthermore, in many situations, on a particular matrix operator, there is an a priori information available. Most eigenvalue algorithms do not utilize all the available information. In this paper, the use of the Lie algebra of matrix operators is suggested for systolic array eigenvector and value computation. After a brief survey of the relevant Lie algebra for such computation, a number of possible Lie signal processing algebra examples are presented.